Given N and M , write an equation using left shift operators whose result will be equal to the product N * M .
Input : First line has 0 < T ≤ 50000 denoting number of test cases.
Next T lines have two integers 0 < N, M ≤ 10¹⁶.Output : For each test case print an equation for N * M resembling
(N << p1) + (N << p2)+ ...+(N << pk) where p1 ≥ p2 ≥ ... ≥ pk and k is minimum.
SAMPLE INPUT SAMPLE OUTPUT 2 2 1 (2<<0) 2 3 (2<<1) + (2<<0)
Time Limit: 1.0 sec
My Solution 1st approach
int dig = (int)(Math.floor(Math.log10(m)/Math.log10(2))+1);
boolean flag = false;
for(long i = dig; i>=0; --i) {
if(((m>>(i-1l)) & 1l) == 1l) {
if(flag)
System.out.print(" + ("+n+ "<<"+(i-1)+")");
else {
System.out.print("("+n+"<<"+(i-1)+")");
flag = true;
}
}
}
Second Approach
boolean[] arr = new boolean[dig];
int i = dig-1;
while(m > 0) {
if((m&1) == 1 ) {
arr[i] = true;
}
i--;
m = m>>1l;
}
int j = dig-1;
for( i = 0; i < dig; ++i) {
if(arr[i]) {
if(flag)
System.out.print(" + ("+n+"<<"+j+")");
else {
System.out.print("("+n+"<<"+j+")");
flag = true;
}
}
j--;
}
In both cases I am getting 5 correct out of 8 and rest 3 are TLE why?
I don't actually see anything in both of your approaches preventing some ten-thousands of products of numbers up to 57 bit to be represented as String
s in one second:
TLE
may be due to System.out.print()
taking an inordinate amount of time.
That said, use a utility like
/** builds <code>n * m</code> in the form
* <code>(n<<p1) + (n<<p2) + ... + (n<<pk)</code>
* using left shift.
* @param n (0 < multiplicand <= 10**16)
* @param m 0 < multiplier <= 10**16
* @return a verbose <code>String</code> for <code>n * m</code>
*/
static String verboseBinaryProduct(Object n, long m) {
int shift = Long.SIZE - Long.numberOfLeadingZeros(m) - 1;
final long highest = 1 << shift;
final StringBuilder binary = new StringBuilder(42);
final String chatter = ") + (" + n + "<<";
final long rest = highest - 1;
while (true) {
if (0 != (highest & m))
binary.append(chatter).append(shift);
if (0 == (rest & m)) {
binary.append(')');
return binary.substring(4);
}
m <<= 1;
shift -= 1;
}
}
and System.out.println(verboseBinaryProduct(n, m));
.
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